Question

A circle with area \blue{16\pi}16πstart color #6495ed, 16, pi, end color #6495ed has a sector with a central angle of \purple{\dfrac{8}{5}\pi}

5
8
​
πstart color #9d38bd, start fraction, 8, divided by, 5, end fraction, pi, end color #9d38bd radians .
What is the area of the sector?
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal rounded to the nearest hundredth.

Answer 1

(64/5)π

Explanation:

Area of the circle: 16π

central angle: (8/5)π

The Area of the circle corresponds to a central angle equal to 2π (the complete circle). Then the following proportion must be satisfied:

16π / x = 2π / (8/5)π

x = [16π * (8/5)π] / 2π

x = (64/5)π